CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Linear Algebra B 2

Code Completion Credits Range Language
801LI2 Z,ZK 4 2P+2C Czech
Garant předmětu:
Lubomíra Dvořáková, Dana Majerová
Lecturer:
Dana Majerová
Tutor:
Dana Majerová
Supervisor:
Department of Software Engineering
Synopsis:

Determinant. Regular matrix, regular operator. Inverse matrix and operator. Inner product, orthogonality, Gramm-Schmidt orthogonalization process. Linear geometry. Eigenvalues, eigenvectors, diagonalization of matrices. Special types of matrices.

Requirements:
Syllabus of lectures:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Syllabus of tutorials:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Study Objective:

Knowledge of basic terms of linear algebra.

Ability to prove mathematical theorems and solve problems of linear algebra, especially work with matrices.

Study materials:

Key references:

[1] Dontová, E. Matematika III. Praha: ČVUT, 1999.

[2] Čížková, L. Sbírka příkladů z matematiky I. Praha: ČVUT, 1999.